6-3: Complex Rational Expressions complex rational expression (fraction) – contains a fraction in its numerator, denominator, or both.

Method 1: Find LCD of all denominators, then multiply both the numerator and denominator by the LCD. LCD = y Distribute  Ex 1:  Multiply numerator and denominator by LCD

Ex 2: LCD = Distribute   or factor  Multiply numerator and denominator by LCD

Ex 3: LCD = Distribute   Factor  Multiply numerator and denominator by LCD

Ex 4: Rewrite with positive exponents Distribute    LCD = or factor  Multiply numerator and denominator by LCD

Ex 5: LCD = Distribute   Multiply numerator and denominator by LCD

Method 2: Simplify the numerator and denominator separately, then use division and multiply by reciprocal. LCD = Ex 6: Add fractions in numerator and denominator. Multiply by reciprocal  

Ex 7:  Factor   Multiply by reciprocal  Simplify the numerator and denominator

Ex 8:  Factor   Multiply by reciprocal  Simplify the numerator and denominator

Ex 9:  Factor   Multiply by reciprocal  Simplify the numerator and denominator

6-3 Summary Method 1: Find LCD of all denominators, then multiply both the numerator and denominator by the LCD. Method 2: Simplify the numerator and denominator separately, then use division and multiply by reciprocal.     